New feature points based on geometric invariants for 3D image registration

We introduce in this paper a new type of feature points of 3D surfaces, based on geometric invariants. We call this new type of feature points the extremal points of the 3D surfaces, and we show that the relative positions of those 3D points are invariant according to 3D rigid transforms (rotation and translation). We show also how to extract those points from 3D images, such as Magnetic Resonance images (MRI) or Cat-Scan images, and also how to use them to perform precise 3D registration. Previously, we described a method, called the Marching Lines algorithm, which allow us to extract the extremal lines, which are geometric invariant 3D curves, as the intersection of two implicit surfaces: the extremal points are the intersection of the extremal lines with a third implicit surface. We present an application of the extremal points extraction to the fully automatic registration of two 3D images of the same patient, taken in two different positions, to show the accuracy and robustness of the extracted extremal points.

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